Modeling Contextualized Knowledge - Leitura de Artigo

Martin Homola, Andrei Tamilin, Luciano Serafini: Modeling contextualized knowledge. In 2nd Workshop on Context, Information and Ontologies (CIAO), 2010

Abstract.  

Most of the knowledge available in the Semantic Web is context dependent. Examples of contextual information that is associated with knowledge are time, topic, provenance, reliability, etc. 

[Dimensões Contextuais]

Recently, several paradigms, tools and languages have been proposed with the aim of adding context awareness into the Semantic Web. That is, enabling representation and reasoning not only with the knowledge alone, but also with the associated contextual information. Examples include RDF quadruples, named graphs, annotated RDF, and contextualized knowledge repositories. These new paradigms introduce a new dimension into knowledge engineering: in addition to individuals, concepts, properties and their relations, we also need to define the set of contexts, and we need to “split” the knowledge between these contexts. 

[Separar ou combinar conhecimento em diferentes contextos]

1 Introduction and Motivation

These are just simple examples showing that most of the knowledge retrievable from the Semantic Web is context dependent. Nevertheless, the information about the context is usually not specified in Semantic Web resources, and when it is so, e.g., by adding attributes like rdfs:comment, owl:AnnotationProperty, etc., this information is completely ignored in the reasoning process. The importance of contextualized knowledge has been widely recognized and this has motivated proposals for extending Semantic Web languages with the possibility of qualifying knowledge w.r.t. some specific contextual dimension. 

[Adicionar comentários ou anotações permitem uma interpretação humana mas não da máquina]

Recently we have proposed a new architecture which accommodates contextual knowledge within the current state-of-the-art semantic web technology [8, 9]. The architecture, called Contextualized Knowledge Repository (CKR), has been also implemented on top of the state-of-the-art RDF triple store OWLIM4. Main features of CKR are as follows:

[Contexto na Web Semântica com RDF]

1. knowledge is contextualized relying on the well studied theories of context [10–15] and this contextualization is implemented inside the current Semantic Web languages without any semantic extension. This is an advantage since we want to rely on the plethora of existing Semantic Web tools;

[Aproveitar ferramentas existentes]   

2. a context is treated as a theory—set of sentences in a logical language, closed under logical consequence—and it is associated with a “point” in a dimensional space. Contexts are also first class objects, and the logic provides terms to denote them;

[A perspectiva teórica do contexto em um espaço multi dimensional]

3. knowledge propagates across contexts according to schematic patterns. This is done through so called qualified concepts and roles which constitute a semantic bridge between different contexts. Lifting axioms are thus hidden from the user and they work automatically. This transfers part of the complexity of the modeling task from the user to the system.

2 The Modeling Domain

FIFA World Cup 2010

2. large part of the knowledge about this event is context dependent.

[As afirmações referentes a eventos são fortemente baseados em contexto, principalmente temporal]

In this case, the triple is valid only in this particular context (i.e., that of the Match 11).

[A tripla não é suficiente para expressar a afirmação e essa perde contexto quando não é possível especificar quando ocorreu]

3 Contextualized Knowledge Repository

According to the context as a box metaphor [16] a context can be viewed as a box. Inside the box is a set of logical statements representing the information associated with this particular context. This is the contextual data. The boundaries of the box are then determined by a set of dimensional values. This
information is the contextual meta data, often simply marked as the outside of the box. For instance, a match between Italy and Paraguay during the FIFA World Cup can be represented by the following context:

[Metáfora de uma caixa onde as afirmações estão dentro e o contexto é o que define os limites, que circunscreve, que delimita]

Although contexts are possibly defined on top of any logical language, we focus on RDF and OWL and hence we will build contexts on top of description logics (DL) [17]. This is due to the fact that OWL itself is built on top of the DL SROIQ [18]. Furthermore we will assume that all the symbols that appear either in the contexts or in dimensional information come from some shared vocabulary Σ.

1. dim(C) is a set of assertions of the form A(C, v) where A is called dimensional attribute and v dimensional value;
2. K(C) is a DL knowledge base in SROIQ or some of its sublanguages.

The set of dimensional values dim(C) of a given context C determines its contextual boundaries. It is also called the dimensional vector of C. ... A context is always specified with a total dimensional vector in which values for each dimension are given. ... This determination may be precise, when all these values are constants. ...    They contain information which is tightly bound with a particular set of dimensional values. ... Besides for primitive contexts we will also make use of context classes. These are more generic contexts that allow us to specify some information which is valid for multiple sets of dimensional values. 

[Contextos primitivos tem valores fixos nos qualificadores. Classes de contextos tem regras para especificar as fronteiras]

Definition 2 (Contextualized Knowledge Repository). A contextualized knowledge repository (CKR) is a pair K =〈D, C〉 where C is a set of contexts, and D is a DL knowledge base such that:

1. D contains n distinct roles A = {A1, . . . , An} called dimensions (or dimensional attributes);
2. for every dimension A ∈ A, D contains a finite set DA called the dimension values of A such that each v ∈ DA is either a constant symbol or a concept in D;
3. for every dimension A ∈ A, D contains a role coversA whose domain and range are the constants of DA;
4. the transitive closure of the relation {〈d, d′〉 | D |= covers(d, d′)}, denoted by ≺A, is a partial order on DA.

Due to the hierarchy of dimensions, the organization of contexts in each CKR is hierarchical as well. Given a CKR K and two contexts C1 and C2 with dim(C1) = d and dim(C2) = e. We say that C1 is covered by C2 if dA ≺A eA for each A ∈ A. This is denoted by C1 ≺ C2 (also d ≺ e).

[O contexto pode apresentar hierarquia, por exemplo para tópicos ou para abrangência espacial]

Context classes do not directly participate in the context hierarchy, as some of their dimensional values are not constants. This corresponds with our intuition that a context class is a special collection of knowledge that belongs into multiple contexts. These contexts are called instances of a given context class.

All basic decision problems such as concept satisfialbility checking and entailment with respect to a CKR knowledge base are decidable, and the complexity of reasoning is not increased when compared to classical DL [9]. The advantages of explicit tracking of knowledge provenance by attaching contextual meta information are apparent. In addition, our system provides means for efficient manipulation of generic information that is valid in multiple contexts using the construct of context class. 

4 Modeling with CKR

In this section we describe how we model the domain of football, in particular the domain of FIFA Would Cup 2010, within a contextualized knowledge repository.
The modeling is composed of three basic components. The first component is the dimension hierarchies and the meta knowledge DFootball. In this knowledge base we represent the structure of the contexts in which we organize all the information about football. The structure of D-Football will be inspired by the structure of the FIFA World Cup 2010 web site. 

[Uma ontologia para representar as dimensões de contexto e suas relações hierárquicas]

The second component of the modeling consists of the context classes which describe types of contexts that we will deal with, such as for instance matches, teams, groups, etc.

Each context class contains all the axioms that should hold in all of its instance-contexts.

[Uma ontologia para as classes de domínio e suas regras de formação]

Finally, the third component of the model are the contexts, with all the specific knowledge.

[Uma ontologia com as instâncias das classes de domínio RELACIONADAS com as dimensões dos contextos ... Fez uso de reificação para essa associação? ]

4.1 Context dimensions

time

[corrente (default), presente, passado, período, ponto no tempo, primeiro, último, recente, concomitante, cobertura temporal (ordenação cronológica)]

location: Geonames

[perto, longe, aqui, próximos, abaixo, acima, dentro, fora, cobertura espacial (hierarquia)]

topic:

[generalização, especialização, relacionado, semelhante, cobertura temática (hierarquia)] 

[Combinando valores das três dimensões é possível criar instâncias de contextos]       

4.2 Context classes

In the CKR architecture, context classes can be viewed as a tool which makes the representation of knowledge more effective. Axioms that are valid in many contexts are asserted in a context class and they are automatically imported by the semantics into all contexts that instantiate the class. For example, in every context that describes a football match, certain general axioms should hold: e.g., there are two teams, one playing against the other, the number of players in the match is eleven or less per team, there is a goalkeeper in each team, etc. Instead of explicitly including all these axioms in each single context associated with a football match, one can create the context class Match containing the axioms and impose that all contexts that describe a particular match are instances of this context class.

[Classes de contexto possuem as regras gerais que podem ser aplicadas a instâncias de contextos]

4.3 Contexts

The declaration of the actual contexts in the repository concludes the modeling process. It is important to stress that when a context is loaded into the CKR, first all matching context classes are identified and then axioms contained in them are copied into the context. 

5 Conjunctive Query Answering over CKR

In this section we will take a look on conjunctive query answering in a CKR. We show how the notion of conjunctive query has to be generalized in order to be useful in a situation involving multiple contexts and we will explain how answers for the conjunctive queries are defined.

[Consultas conjuntivas precisam ser especificadas com contexto]

Definition 4 (Contextual Conjunctive Query). A contextual conjunctive query (CCQ) over a CKR is an expression of the form Q(x) ← ∃y ∧n i=1 di : φi(x, y) where for each i, di is a possibly partial dimensional vector, and φi(x, y) is a conjunction of unary and binary predicates taking variables from x and y. If x is empty then the query is called boolean. If for each i, di is a total dimensional vector then the query is said to be fully contextualized.  

In CKR, queries can span over multiple contexts with different conceptualizations and hence the result can be seen as a mash-up of knowledge from different contexts. We will make use of substitution and completion. By φ[x/a] we will understand the expression derived from φ in which each element of x is replaced by the respective element of a. Given two dimensional vectors d and e, by d + e we will understand a completed vector which contains all elements of d plus the elements of e for those dimensions which d is missing. The semantics of CCQ is defined as follows.

Definition 5. A fully contextualized boolean CCQ Q() ← ∃y ∧n i=1 di : φi(y) is said to be entailed by a CKR K, if for each model I of K there is a substitution u such that Idi |= φ(y)[y/u]. This is denoted by K |= Q(). 

The expression e : a formed by a dimensional tuple e and a tuple of constants a is an answer for a CCQ Q(x) ← ∃y ∧k
i=1 di : φi(x, y) with respect to a CKR
K, if K |= ∧k
i=1 di + e : φi(x, y)[x/a].

[Não consigo entender completamente essa formalização]

Q(x, y) ← 〈2010, World, FIFA WC〉 : Goalkeeper(x) ∧ in Squad(x, y)

[Todos os goleiros convocados com suas equipes do contexto (tópico, abrangência georgráfica, tempo): (Copa do Mundo, Mundial, 2010)]

Q(x) ← 〈World, FIFA WC〉 : Goalkeeper(x) ∧ in Squad(x, Team Italy)

[Todos os goleiros da Itália do contexto (tópico, abrangência geográfica): (Copa do Mundo, Mundial), em qualquer contexto temporal. A informação recuperada deve estar contextualizada no tempo]

Q(x, y) ← ∃z〈2010, World, FIFA WC〉 : in Squad(x, y) ∧〈2010, World〉 : in Lineup(z, x)

[Todos os goleiros que efetivamente entraram em campo com suas equipes do contexto (tópico, abrangência georgráfica, tempo): (Copa do Mundo, Mundial, 2010). A informação recuperada deve estar contextualizada em subtópicos]  

6 Related Work

Another notable example extensively modeling football domain is Freebase. Freebase is a massive collaboratively-edited RDF-exportable knowledge base of facts about people, organizations, events, etc. The knowledge base is organized into domains (e.g., sport disciplines, politics, etc.), grouping relevant
types (e.g., sport championships, clubs and players, politicians and parties, etc.).

Types have properties (e.g., Date of birth for type Person), and can be organized in inheritance hierarchies (e.g., Football Player type extends generic type Person) allowing for property inheritance. For example, for representation of facts about 2010 FIFA World Cup Freebase contains a dedicated type
FIFA World Cup 201013. One of the distinguishing characteristics of Freebase is extensive use of reification in order to support compound multi-dimensional properties, allowing to assign contextually bounded values. An example of such a compound property is Football Player Match Participation allowing to assert for a given match a player and a team he plays.

[Freebase é um KG aberto que faz uso de reificação. Alternativa é criar indivíduos diferentes para cada contexto e agrupar em uma SuperClasse]

7 Conclusion

...(1) knowledge is organized in contexts which are hierarchically sorted according to the coverage relation defined with respect to the contextual metadata; (2) the coverage relation is itself formalized in an RDF/OWL ontology, which introduces flexibility on the structure of contexts and it allows to reason, not only inside the contexts but also on the contextual organization; (3) with context classes generic knowledge that is valid in multiple contexts can be asserted effectively and with minimal redundancy; (4) so called qualified concepts and roles allow for fully automated knowledge “importing” between the contexts that relies on their hierarchical structure, it is intuitive to use, and whose technicalities are hidden from the user; (5) contextual conjunctive queries provide a flexible data retrieval mechanism in which also contextual metadata are returned with the answers and furthermore the querying can be also refined by such metadata.        

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Mais informações extraídas de https://dkm.fbk.eu/technologies/theoretical-frameworks/ckr-contextualized-knowledge-repository/

SPARQL-based contextual queries, supporting the constraining and the extraction of knowledge from multiple contexts by extending SPARQL with a CONTEXT keyword;

[Foi necessário estender a linguagem SPARQL]

Answer Set Programming based reasoning methods for instance checking and conjunctive query answering for CKRs with defeasible axioms;

[Consultas definidas previamente. Não são consultas abertas.]

Implementation of CKR defined as SPARQL-based forward rules over multiple RDF named graphs. The framework is implemented over an extension of Sesame called SPRINGLES (SParql-based Rule Inference over Named Graphs Layer Extending Sesame), which supports the specification and execution of inference over Sesame RDF repositories.

 

Querying. Contextual queries in CKR are an extension of SPARQL where the keyword CONTEXT constrains the queried context. For instance, Figure 1b presents a contextual query to extract all the winners of 2011 football competitions. Query answering is performed after the CKR closure operation is applied.